A sequential recursive algorithm and hierarchical framework for power system carbon measurement considering carbon emission flow losses

Abstract Accurate measurement of carbon footprints for electricity consumption is crucial for equitable allocation of emission responsibility and grid decarbonization. This paper proposes a novel sequential recursive algorithm to address spatiotemporal inaccuracies and carbon imbalance in conventional approaches. The algorithm dynamically propagates carbon intensity from upstream generators to downstream loads, explicitly incorporating the impact of transmission losses. By integrating power flow physics with a dynamic proportional sharing principle, this paper establishes a loss-inclusive metrological model. This model converts lossy networks into lossless equivalents through equivalent power transformation, ensuring strict carbon conservation between generation and consumption. Leveraging the small-world topology of power systems, a hierarchical computational architecture is developed to enable cross-regional carbon tracking under data isolation constraints. Comprehensive validation demonstrates a carbon balance in IEEE 14/118-node systems, computational equivalence between hierarchical and global methods for 200-node networks, and a strict carbon balance that accurately calculates the carbon intensity of all nodes while maintaining data isolation in 1000-node systems. This framework provides a traceable measurement foundation for decarbonization strategies and multi-regional emission allocation, while supporting accurate cross-regional carbon measurement as a core of carbon markets. It significantly advances metrological accuracy in large-scale power systems.